“…Duan [ 6 , 7 ] studied the effect of each slag component on the activities of Al 2 O 2 and TiO 2 , and determined an appropriate slag to be used for ESR of superalloys based on experiments and thermodynamics. Jiang [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ] investigated the thermodynamic equilibrium of 3[Ti] + 2(Al 2 O 3 ) = 4[Al] + 3(TiO 2 ) and the effect of slag components on activities of Al 2 O 2 and TiO 2 in CaF 2 -CaO-MgO-Al 2 O 3 -TiO 2 slag system, and then TiO 2 in slag was calculated to control the titanium and aluminum contents in ESR ingot. However, the above researches [ 17 , 18 , 19 , 20 , 21 ] did not comprehensively consider the physical properties and thermodynamic equilibrium of 3[Ti] + 2(Al 2 O 3 ) = 4[Al] + 3(TiO 2 ).…”